An extended-range electric vehicle powertrain provides one or more electric-vehicle (EV) modes. In an EV mode, a high-voltage electric traction motor is powered via a rechargeable battery pack. Output torque from the electric traction motor is typically delivered to a transmission having one or more planetary gear sets. Braking energy may be recovered during a regenerative braking event to recharge the battery pack. When a state of charge of the battery pack is depleted, the EV range of the vehicle may be extended by selective operation of a small internal combustion engine, with engine torque used to generate additional electricity as needed.